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Some of the recent advances in the theory of thin airfoils are presented with particular reference to extensions of the theory to three dimensional flows and to supersonic speeds. The problem discussed herein is the calculation of the small disturbance velocities u, v, and w in the external field produced by the flight velocity V of the airfoil.
The relation of Whitcomb's area rule to the linear formulas for wave drag at slightly supersonic speeds is discussed. By adopting an approximate relation between the source strength and the geometry of a wing-body combination, the wave drag theory is expressed in terms involving the areas intercepted by oblique planes or Mach planes. The resulting formulas are checked by comparison with the drag measurements obtained in wind tunnel experiments and in experiments with falling models in free air. Finally, a theory for determining wing-body shapes of minimum drag at supersonic Mach numbers is discussed and some preliminary experiments are reported.
Conventional treatments of accelerated motion in the theory of relativity have led to certain difficulties of interpretation. Certain reversals in the apparent gravitational field of an accelerated body may be avoided by simpler analysis based on the use of restricted conformal transformations. In the conformal theory the velocity of light remains constant even for experimenters in accelerated motion. The problem considered is that of rectilinear motion with a variable velocity. The motion takes place along the x or x' axis of two coordinate systems.
Fluid-dynamic moment equations, based on a kinetic hierarchy system, are derived governing the interaction between turbulent and thermal fluctuations. The kinetic theory is shown to reduce the inherent complexity of the conventional formalism of compressible turbulence theory and to minimize arbitrariness in formulating the closure condition.
Aerodynamic flutter and a re-written computer program for its study are discussed. Data cover: (1) lifting surface theory with boundary layer, (2) incompressible, two dimensional, unsteady flow with control surfaces, (3) improved unsteady theory, (4) combined transonic airfoil thickness and shear layer thickness effects, and (5) bending-torsion flutter calculations.
A nonlinear dynamic theory is developed for the formation of photorefractive volume phase holograms. A feedback mechanism existing between the photogenerated field and free-electron density, treated explicitly, yields the growth and saturation of the space-charge field in a time scale characterized by the coupling strength between them. The expression for the field reduces in the short-time limit to previous theories and approaches in the long-time limit the internal or photovoltaic field. Additionally, the phase of the space charge field is shown to be time-dependent.
It is shown that density and pressure throughout the thermosphere can be adequately described in a logarithmic expansion that provides a sound basis for the application of perturbation theory. This expansion eliminates most of the important nonlinearities associated with density variations. On the basis of this expansion, the validity of perturbation theory can be extended to cover a large variety of atmospheric conditions in which the relative temperature amplitude is less than 0.5 and wind velocities are significantly less than the speed of sound.
A theory for the pitch-angle scattering of cosmic rays in a turbulent magnetic field can be derived from first principles by applying both the quasi-linear and adiabatic approximations to the master equation for the ensemble averaged distribution function. A proof of the failure of these approximations, taken together, is given. Some predictions of the quasi-linear theory, are given. New wave-like propagation modes have been discovered.
Papers given on the modulation of galactic cosmic rays by the solar wind at the 14th International Cosmic Ray Conference are reviewed. Some of the topics treated in this review are Pioneer and Helios radial gradient measurement, heliolatitude effects in modulation models, diffusion (scattering) theory - including pitch angle diffusion diagrams - solar flare particle transport theory and cosmic ray fluctuations at neutron monitor energies.
Various existing unsteady aerodynamic strip theories which have been developed in the past for both fixed and rotary wing aeroelastic analyses are modified in the paper so as to make them applicable to the coupled flap-lag-torsional aeroelastic problem of a rotor blade in hover. These corrections are primarily due to constant angle of attack, constant inflow and variable free stream velocity due to lead-lag motion. Next, the modified strip theories are incorporated in a coupled flap-lag-torsional aeroelastic analysis of the rotor blade in hover and the sensitivity of the aeroelastic stability boundaries to the aerodynamic assumptions is examined.
Potential vorticity theory is developed in a description of an equivalent potential temperature topography, and a new theory suited to the description of scale interaction is elaborated. Macroscale triggering of ageostrophic flow fields at the mesoscale, in turn leading to release of convective instability along narrow zones at the microscale, is examined. Correlation of appreciable decrease in potential vorticity with such phenomena as cumulonimbi, tornados, and duststorms is examined. The relevance of a multiscale energy-momentum cascade in numerical prediction of severe mesoscale and microscale phenomena from radiosonde data is reviewed. Hypotheses for mesoscale dynamics are constructed.
The aerodynamic interaction between the wing and an inviscid upper-surface blowing (USB) thick jet with Mach number nonuniformity is treated within the framework of a linear inviscid subsonic compressible flow theory. A two-vortex-sheet model for the jet surface is used to represent the induced flowfields inside and outside the jet. Comparison of the predicted results with experimental data shows good agreement in lift, induced drag, and pitching moment. It is shown that the thin jet flap theory is inadequate for USB configurations with thick jet.
A semi-empirical entrainment theory was employed to correlate the measured temperature depression, Delta T, in a developed cavity for a venturi. This theory correlates Delta t in terms of the dimensionless numbers of Nusselt, Reynolds, Froude, Weber and Peclet, and dimensionless cavity length, L/D. These correlations are then compared with similar correlations for zero and quarter caliber ogives. In addition, cavitation number data for both limited and developed cavitation in venturis are presented.
Sampled analog comb filter using a recursive filter implementation was studied. Charge transfer device delay lines were used as the delay elements. The similarities and differences between sampled analog recursive filter and digital recursive filter were pointed out. Both canceller type and integrator type comb filter using the first order or the second order canonical circuits were studied. Experimental results of frequency response are presented to show their difference from that of digital filters. A theoretical analysis was presented based essentially on the digital filter theory but modified to take into account the differences described above. The usefulness of this theory in analyzing the comb filter characteristics was discussed. Several applications of both the canceller type comb filter and the integrator type comb filter were demonstrated.
A multivariable control design procedure based on output feedback regulator (OFR) theory is applied to the F100 turbofan engine. Results for the OFR design are compared to a design based on linear quadratic regulator (LQR) theory. The OFR feedback control is designed in the full order state space and thus eliminates any need for model reduction techniques. Using the performance measure and control structure of the LQR design, an equivalent OFR feedback control is obtained. The flexibility of the OFR as a control design procedure is demonstrated, and differing feedback control structures are evaluated.
Finite difference equations are derived for sound propagation in a two dimensional, straight, soft wall duct with a uniform flow by using the wave envelope concept. This concept reduces the required number of finite difference grid points by one to two orders of magnitude depending on the length of the duct and the frequency of the sound. The governing acoustic difference equations in complex notation are derived. An exit condition is developed that allows a duct of finite length to simulate the wave propagation in an infinitely long duct. Sample calculations presented for a plane wave incident upon the acoustic liner show the numerical theory to be in good agreement with closed form analytical theory. Complete pressure and velocity printouts are given to some sample problems and can be used to debug and check future computer programs.
In situ satellite observations of type III burst exciters at 1 AU show that the beam does not evolve into a plateau in velocity space, contrary to the prediction of quasilinear theory. The observations can be explained by a theory that includes mode coupling effects due to excitation of the parametric oscillating two-stream instability and its saturation by anomalous resistivity. The time evolution of the beam velocity distribution is included in the analysis.
A kinetic theory is presented for boundary layers associated with MHD tangential 'discontinuities' in a collisionless magnetized plasma, such as those observed in the solar wind. The theory consists of finding self-consistent solutions of Vlasov's equation and Maxwell's equation for stationary one-dimensional boundary layers separating two Maxwellian plasma states. Layers in which the current is carried by electrons are found to have a thickness of the order of a few electron gyroradii, but the drift speed of the current-carrying electrons is found to exceed the Alfven speed, and accordingly such layers are not stable. Several types of layers in which the current is carried by protons are discussed; in particular, cases are considered in which the magnetic-field intensity, direction, or both, changed across the layer. In every case, the thickness was of the order of a few proton gyroradii, and the field changed smoothly, although the characteristics depended somewhat on the boundary conditions. The drift speed was always less than the Alfven speed, consistent with stability of such structures. These results are consistent with observations of boundary layers in the solar wind near 1 AU.