Report discussing theoretical basis of the acoustics of a moving nonhomogeneous medium. Experiments that illustrate or confirm some of the theoretical explanation or derivation of these acoustics are also included.
Report presenting an investigation to determine the carry loads and mutual aerodynamic interference effects from high-speed wind-tunnel tests and the drop characteristics of the X-15 through the B-52 flow field from low-speed dynamic-model drop tests and six-degree-of-freedom calculations. The X-15 installation was found to increase drag at cruise conditions by approximately 15 percent.
"The unsteady aerodynamic forces, [based on two-dimensional incompressible flow considerations], are determined for an unstaggered cascade, the blades of which are vibrating in phase in an approach flow parallel to the blades" (p. 1).
The influence of the deflected flow caused by the fuselage (especially by unsymmetrical attitudes) on the lift and the rolling moment due to sideslip has been discussed for infinitely long fuselages with circular and elliptical cross section. The aim of this work is to add rectangular cross sections and, primarily, to give a principle by which one can get practically usable contours through simple conformal mapping. In a few examples, the velocity field in the wing region and the induced flow produced are calculated and are compared with corresponding results from elliptical and strictly rectangular cross sections.
The technical memorandum briefly summarizes the growth of interest in aeroelastic phenomena as aircraft speed increased and wing designs changed for faster aircraft. Different types of aircraft vibrations are then introduced, and the mathematical basis for the theory behind them is described. Special attention is given to static oscillations, wing flutter, and the flutter of skin panels. The last section of the memorandum deals with the prevention of flutter by design specifications.
From Introduction: "The problem of thrust increase for jet engines by air mixture to the exhaust jet was introduced into aviation techniques by the suggestions of Melot (ref.1). Due to a too general interpretation of several theoretical investigations of A. Busemann (ref.2), so far no practical use has been made of these suggestions. The following considerations show that, in the case of low-pressure mixing according to Melot's suggestions, probably no thrust increase of technical significance will occur for the flight speeds of interest (however, the low-pressure mixture is highly promising for ground test setups and for special power plants of relatively slow sea and land vehicles."
From Summary: "The author first sets forth some observations about the theory of models. Then he established certain general criteria for the construction of dynamically similar models in water and in air, through reference to the perfect fluid equations and to the ones pertaining to viscous flow. It is, in addition, pointed out that there are more cases in which the analogy is possible than is commonly supposed."
From Introduction: "The present report, therefore, deals first, with the distribution of the amplitude of the disturbance over the flow section, that is, the calculation of the characteristic functions and second, with the study of the energy distribution and energy balance of the disturbance motion. The investigations are based upon the disturbances of the laminar flow past a flat plate which are situated exactly at the boundary between amplification and damping (neutral oscillations)."
The problem of shimmy of a castering wheel, such as the nose wheel of a tricycle gear airplane, is treated analytically. The flexibility of the tire is considered to be the primary cause of shimmy. The rather simple theory developed agrees rather well with previous experimental results. The author suggests that shimmy may be eliminated through a suitable choice of landing gear dimensions in lieu of a damper.
The report describes a brief review is made of improvements to an experimental apparatus for time and space correlation designed for study of turbulence. Included is a description of the control of the measurements and a few particular applications.
The method of coordinate perturbation is applied to the unsteady flow of a compressible fluid in ducts of variable cross section. Solutions, in the form of perturbation series, are obtained for unsteady flows in ducts for which the logarithmic derivative of area variation with respect to the space coordinate is a function of the 'smallness' parameter of the perturbation series. This technique is applied to the problem of the interaction of a disturbance and a shock wave in a diffuser flow. It is found that, for a special choice of the function describing the disturbance, the path of the shock wave can be expressed in closed form to first order. The method is then applied to the determination of the flow field behind a shock wave moving on a prescribed path in the x,t-plane. Perturbation series solutions for quite general paths are developed. The perturbation series solutions are compared with the more exact solutions obtained by the application of the method of characteristics. The approximate solutions are shown to be in reasonably accurate agreement with the solutions obtained by the method of characteristics.
"The shell shall be considered as a three-dimensional continuous medium; for the coordinate surface, the middle surface of the shell shall be assumed parallel to the bounding surfaces. Let alpha and beta be the curvilinear orthogonal coordinates of this surface, coinciding with the lines of principal curvatures, and gamma the distance along the normal from the point (alpha,beta) of the coordinate surface to any point (alpha, beta, gamma) of the shell" (p. 1).
For compressible flow with friction in a cylindrical pipe the momentum, continuity, and heat-transfer equations are examined to determine whether an increase in Mach number ("thermal" Laval nozzle) is obtainable through heat conduction from the gas through the pipe walls. The analysis is based on the assumption that the wall temperature is negligibly small in comparison with the stagnation temperature of the gas. The analysis leads to a negative result. When the gas cooling is increased by also considering radiation to the wall, a limited region at high temperatures is obtained where Mach number increases were theoretically possible. Obtaining this condition practically is considered impossible.
From Introduction: "The fundamental, practically the most important branch of the modern mechanics of a viscous fluid or a gas, is that branch which concerns itself with the study of the boundary layer. The presence of a boundary layer accounts for the origin of the resistance and lift force, the breakdown of the smooth flow about bodies, and other phenomena that are associated with the motion of a body in a real fluid. The concept of boundary layer was clearly formulated by the founder of aerodynamics, N. E. Joukowsky, in his well-known work "On the Form of Ships" published as early as 1890."
"The vortices forming in flowing water behind solid bodies are not represented correctly by the solution of the potential theory nor by Helmholtz's jets. Potential theory is unable to satisfy the condition that the water adheres at the wetted bodies, and its solutions of the fundamental hydrodynamic equations are at variance with the observation that the flow separates from the body at a certain point and sends forth a highly turbulent boundary layer into the free flow. Helmholtz's theory attempts to imitate the latter effect in such a way that it joins two potential flows, jet and still water, nonanalytical along a stream curve" (p. 1).
A comparatively rapid method is presented for determining theoretically the bending stresses of helicopter rotor blades in forward flight. The method is based on the analysis of the properties of a vibrating beam, and its uniqueness lies in the simple solution of the differential equation which governs the motion of the bent blades.
"Graphs and formulas are given with the aid of which all the aerodynamic coefficients required for computing the lateral dynamic stability can be determined. A number of numerical examples are given for obtaining the stability derivatives and solving the characteristic-stability equation. Approximate formulas are derived with the aid of which rapid preliminary computations may be made and the stability coefficients corrected for certain modifications of the airplane" (p. 1).
"The idea is advanced of making a supersonic nozzle by producing one, two, or three successive turns of the whole flow; with the result that the wall contour can be calculated exactly by means of the Prandtl-Meyer "Lost Solution" (p. 1).
"For application in practice for annular radiator fairings and similar arrangements, two new classes of circular cowls are developed by theoretical method, and investigated in a systematic test series regarding their behavior under various working conditions" (p. 1).
"It is shown how one may obtain, in a simple manner, the forms of ring-shaped bodies from existing tables of functions according to the customary method of superposition of flow due to singularities and parallel flow. A number of examples of the forms and pressure distributions of annular source bodies with and without hub body are given, and the inlet conditions of such ring-shaped cowlings are investigated. Furthermore, the annular bodies of finite length are indicated that correspond to Joukowsky profiles for the two-dimensional case" (p. 1).
The investigations carried out in a previous report (NACA TM 1325) concerning the flow about ring-shaped cowlings were extended by taking a circulation about the cowling into consideration. The present second report treats bodies of infinite length with approximately smooth entrance. The circulation was caused by distributing vortex rings of constant density over a stream surface extending to infinity. Furthermore, the influence of a hub body on such cowlings was dealt with.
"The present report presents as a supplement to the fourth report (available as ATI 5045, Air Materiel Command) in the series of investigations concerning the flow about ring-shaped cowlings further wind-tunnel measurements on inlet devices which are to show the influence of the radius of the nose of the cowling on the flow conditions. Moreover, a simple rule for the design of such arrangements, containing a hub in the interior, is suggested" (p. 1).
"The measurements of part V (reference 1) of this series of reports, which concerned comparatively long ring profiles, are supplemented by measurements on shorter rings as they are used for shrouded propellers and cowlings of ring-shaped radiators. Mass-flow coefficients and profile drags are given. Furthermore, it has to be determined how far the potential theory describes the flow phenomenon with sufficient accuracy and whether the present theory for the calculation of thin annular profile yields useful profile forms and is suitable for determination of the mass flow for thick profiles" (p. 1).
The dependence of the maximum incremental velocities and air forces on a circular cowling on the mass flow and the angle of attack of the oblique flow is determined with the aid of pressure-distribution measurements. The particular cowling tested had been partially investigated in NACA TM 1327.
"The influence of thickness and length of a hub projecting from an inlet opening was investigated on one of the two new classes of circular cowls reported in NACA TM 1360" (p. 1).
Planar stress-strain relations and bending stress-strain relations are presented for elastic orthotropic plates and specialized to plywood. These relations are used to derive the differential equation and energy expression for the buckling of orthotropic rectangular plates whose principal stiffness directions are not parallel to the plate edges. Buckling analyses are made for the case of pure compression and pure shear of a long plate-strip.
A basic theoretical and experimental investigation is made of the shimmy behavior of a swiveling landing gear, the experimental tests being conducted with a small wheel mounted over a continuous belt. Effects of wheel loading, rolling velocity, rearward position of the wheel with respect to the swivel axis, tire elasticity, and torsional flexibility of the fuselage are investigated both experimentally and theoretically. A major theoretical conclusion is that the motion of a landing gear moving in a straight line without fuselage elasticity is stable for a sufficiently large rearward position of the wheel behind the swivel axis, and this conclusion is well verified quantitatively by the experimental data.
Jet boundary corrections for partly open and partly closed elliptical wind tunnels for the cases of one and two solid wall segments are presented. Also presented are the combinations of model span and extent of the solid portion of the tunnel wall for which the average correction factor is zero.
The Euler equations for the rotation of a solid body are applied to the problem of the motion of ultracentrifuges. Particular attention is paid to the problem of the passage of an ultracentrifuge rotor through the critical velocity. The factors that affect the passage of rotors through the critical point are stressed.
The effect of various pre-treatments on the elastic strain coefficient (alpha) (defined as the reciprocal of the modulus of elasticity E) (Epsilon) and on the mechanical hysteresis of copper has been investigated. Variables comprising the pre-treatments were pre-straining by stretching in a tensile testing machine and by drawing through a die, aging at room and elevated temperatures and annealing. The variation of the elastic strain coefficient with test stress was also investigated.
The displacement effect of the boundary layer on the outer frictionless flow is discussed for both steady and unsteady flows. The analysis is restricted to cases in which the potential flow pressure distribution remains valid for the boundary-layer calculation. Formulas are given for the dependence of the pressure drag, friction drag, and total drag of circular cylinders on the time from the start of motion for cases in which the velocity varies as a power of the time. Formulas for the locations and for the time for the appearance of the separation point are given for two dimensional bodies of arbitrary shape.
For determination of the elastic constants of airplane tires which are required for the numerical calculations of the shimmy properties of nose and tail wheels, deformation measurements were carried out on four different tires. For this purpose, the tires were loaded in each case with a normal load and then with a lateral force, a tangential force, and a moment. Moreover, the weight and the mass moment of inertia about a vertical axis were determined for the various tires.
The subject of the development of German hollow turbine blades for use with internal cooling is discussed in detail. The development of a suitable blade profile from cascade theory is described. Also a discussion of the temperature distribution and stresses in a turbine blade is presented. Various methods of manufacturing hollow blades and the methods by which they are mounted in the turbine rotor are presented in detail.
Memorandum presenting an investigation of boundary-layer suction and its favorable effect in deferring transition points as long as possible in order to avoid turbulence.
A theoretical investigation is made of the development of a laminar boundary layer behind a suction slot that is assumed to cut off part of the boundary layer without exerting any sink effect. The development, which is approximate, is based on the heat conduction equation. The heat conduction equation enters the analysis through a linearization of the Prandtl-Mises form of the boundary-layer equation.
The turbulent diffusion of a hot air jet in air can be divided into two zones, the core and the transition zone. The present report deals with the transitional zone.
"So far, very careful investigations have been made regarding the flight properties, in particular the static and dynamic stability, of engine-propelled aircraft and of untowed gliders. In contrast, almost no investigations exist regarding the stability of airplanes towed by a towline. Thus, the following report will aim at investigating the directional stability of the towed airplane and, particularly, at determining what parameters of the flight attitude and what configuration properties affect the stability" (p. 1).
"Drop hammer tests with different shock strut models and shock strut oils were performed at temperatures ranging to -40 C. The various shock strut models do not differ essentially regarding their springing and damping properties at low temperatures; however, the influence of the different shock strut oils on the springing properties at low temperatures varies greatly" (p. 1).
"Static tensile test results are presented for specimens of 2014-T6, 2024-T4, 6061-T6, and 7075-T6 aluminum alloy containing fatigue cracks. The results are found to be in good agreement with the results reported for similar tests from other sources. The results indicate that the presence of a fatigue crack reduced the static strength, in all cases, by an amount larger than the corresponding reduction in net area; the 6061-T6 alloy specimens were least susceptible to the crack and the 7075-T6 alloy specimens were most susceptible" (p. 1).
Turbulence was generated by using screens, and the turbulence percentage was measured by a hot-wire anemometer both in the boundary layer and the free stream. The local heat-transfer coefficient was measured at 12 locations along the plate for the cases of various turbulence levels. The transition Reynolds number from laminar to turbulent flow decreases as the main-stream turbulence level increases. In the range of laminar heat transfer the effect of turbulence in the main flow was not great, but in the range of turbulent heat transfer the heat-transfer coefficient increases according to the increase of turbulence.
"For the determination of the flow velocity one is accustomed to measure the impact pressure, i.e., the pressure intensity in front of an obstacle. In incompressible fluids the impact pressure is yv(sup 2)/2g if the influence of viscosity can be neglected. Such an influence is appreciable, however, when the Reynolds number corresponding to impact tube radius is under about 100, and must consequently be considered, if the velocity determination is not to be faulty" (p. 1).
Intense sound waves with a resonant frequency of 5000 cycles per second were imposed on a stationary propane-air flame issuing from a nozzle. In addition to a slight increase of the flame velocity, a fundamental change both in the shape of the burning zone and in the flow pattern could be observed. An attempt is made to explain the origin of the variations in the flame configuration on the basis of transition at the nozzle from jet flow to potential flow.
"In dusty air flows occurring in industrial practice in transport by air pressure of friable materials, in the drying, annealing, and so forth, of a pulverized solid mass in suspension, and in other processes, the concentration of solid particles usually has a magnitude of the order of 1 kg per 1 kg of air. At such a concentration, the ratio of the volume of the particles to the volume of the air is small (less than one-thousandth part). However, regardless of this, the presence of a solid admixture manifests itself in the rules for the velocity distribution of the air in a dusty air flow" (p. 1).
In some applications, aluminum alloys are subjected to intermittent heating at elevated temperature. It is generally considered that the effects of such intermittent heating are cumulative, and therefore are the same as if the heating had been continuous for the same total length of time. The object of these tests was to determine the effects of intermittent and continuous heating at 300 and 400 F, for total periods of 100 and 200 hr, upon the tensile properties of 2024-T4 and 6061-T6 alloy rolled-and-drawn rod and 7075-T6 alloy extrusions, at room temperature and at the temperature of heating.
"Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions" (p. 1).
"In considering the motion of the rocket, at each instant of time only the state of those material particles which at that instant are within the control surface passing through the exterior surface of the body of the rocket and the exit section of the nozzle shall be included. In order to obtain the equations of motion of the rocket, the following procedure is used. An arbitrary but fixed instant of time is considered" (p. 1).
The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
This document presents equations for the two-dimensional stationary problem of gas dynamics, and uses them to derive other equations, including equations for vorticity.
"With the aid of the method of small oscillations which was used successfully in the investigation of the stability of laminar velocity distributions in the presence of two-dimensional perturbations, the excitation of the unstable perturbations for the Hartree velocity distributions occurring in plane boundary-layer flow for decreasing and increasing pressure is calculated as a supplement to a former report. The results of this investigation are to make a contribution toward calculation of the transition point on cylindrical bodies" (p. 1).
DVL experimental and analytical work on the cooling of turbine blades by using ram air as the working fluid over a sector or sectors of the turbine annulus area is summarized. The subsonic performance of ram-jet, turbo-jet, and turbine-propeller engines with both constant pressure and pulsating-flow combustion is investigated. Comparison is made with the performance of a reciprocating engine and the advantages of the gas turbine and jet-propulsion engines are analyzed. Nacelle installation methods and power-level control are discussed.
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