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Free Convection Under the Conditions of the Internal Problem

Description: Convection is called free is the stresses (including the normal pressure) to which the fluid is subjected at its boundaries do not perform mechanical work, that is, if all the boundaries of the fluid are stationary. The case where this is not true is termed forced convection. It corresponds to the action on the fluid of some mechanical suction pumping the fluid.
Date: April 1, 1958
Creator: Ostroumov, G. A.

Stability of Cylindrical and Conical Shells of Circular Cross Section, with Simultaneous Action of Axial Compression and External Normal Pressure

Description: We consider in this report the determination of the upper limit of critical loads in the case of simultaneous action of a compressive force, uniformly distributed over plane cross sections, and of isotropic external normal pressure on cylindrical or conical shells of circular cross section. As a starting point we use the differential equations for neutral equilibrium of conical shells which have been used for the solution of the problem of stability of conical shells under torsion and under axial compression; upon solution of the problem it is possible to satisfy all boundary conditions, in contrast to the report where no attention is paid to the fulfillment of the boundary conditions, and to the report where only part of the boundary conditions are satisfied by solution of the problem according to Galerkin's method. Approximate formulas are used for the determination of the critical external normal pressure with simultaneous action of longituninal compression. Let us note that the formulas suggested in reference 5 are not well founded and may lead, in a number of cases, to a substantial mistake in the magnitude of the critical load.
Date: April 1, 1958
Creator: Mushtari, K. M. & Sachenkov, A. V.

The Interaction of a Reflected Shock Wave with the Boundary Layer in a Shock Tube

Description: Ideally, the reflection of a shock from the closed end of a shock tube provides, for laboratory study, a quantity of stationary gas at extremely high temperature. Because of the action of viscosity, however, the flow in the real case is not one-dimensional, and a boundary layer grows in the fluid following the initial shock wave. In this paper simplifying assumptions are made to allow an analysis of the interaction of the shock reflected from the closed end with the boundary layer of the initial shock afterflow. The analysis predicts that interactions of several different types will exist in different ranges of initial shock Mach number. It is shown that the cooling effect of the wall on the afterflow boundary layer accounts for the change in interaction type. An experiment is carried out which verifies the existence of the several interaction regions and shows that they are satisfactorily predicted by the theory. Along with these results, sufficient information is obtained from the experiments to make possible a model for the interaction in the most complicated case. This model is further verified by measurements made during the experiment. The case of interaction with a turbulent boundary layer is also considered. Identifying the type of interaction with the state of turbulence of the interacting boundary layer allows for an estimate of the state of turbulence of the boundary layer based on an experimental investigation of the type of interaction. A method is proposed whereby the effect of the boundary-layer interaction on the strength of the reflected shock may be calculated. The calculation indicates that the reflected shock is rapidly attenuated for a short distance after reflection, and this result compares favorably with available experimental results.
Date: March 1, 1958
Creator: Mark, Herman

Investigation of Aperiodic Time Processes with Autocorrelation and Fourier Analysis

Description: Autocorrelation and frequency analyses of a series of aperiodic time events, in particular, filtered noises and sibilant sounds, were made. The position and band width of the frequency ranges are best obtained from the frequency analysis, but the energies contained in the several bands are most easily obtained from the autocorrelation function. The mean number of zero crossings of the time function was determined from the curvature of the latter function in the vicinity of the zero crossing, and also with the aid of a decimal counter. The second method was found to be more exact.
Date: March 1, 1958
Creator: Exner, Marie Luise

Evaporation, Heat Transfer, and Velocity Distribution in Two-Dimensional and Rotationally Symmetrical Laminar Boundary-Layer Flow

Description: 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.
Date: February 1, 1958
Creator: Froessling, Nils

Impact on a Compressible Fluid

Description: Upon impact of a solid body on the plane surface of a fluid, there occurs on the vetted surface of the body an abrupt pressure rise which propagates into both media with the speed of sound. Below, we assume the case where the speed of propagation of sound in the body which falls on the surface of the fluid may be regarded as infinitely large in comparison with the speed of propagation of sound in the fluid; that is, we shall assume that the falling body is absolutely rigid. IN this case, the entire relative speed of the motion which takes place at the beginning of the impact is absorbed by the fluid. The hydrodynamic pressures arising thereby are propagated from the contact surface within the fluid with the speed of sound in the form of compression and expansion waves and are gradually damped. After this, they are dispersed like impact pressures, reach ever larger regions of the fluid remote fran the body and became equal to zero; in the fluid there remain hydrodynamic pressures corresponding to the motion of the body after the impact. Neglecting the forces of viscosity and taking into account, furthermore, that the motion of the fluid begins from a state of rest, according to Thomson's theorem, we may consider the motion of an ideal compressible fluid in the process of impact to be potential. We examine the case of impact upon the surface of a ccmpressible fluid of a flat plate of infinite extent or of a body, the immersed part of the surface of which may be called approximately flat. In this report we discuss the first phase of the impact pressure on the surface of a fluid, prior to the appearance of a cavity, since at this stage the hydrodynamic pressures reach their ...
Date: February 1, 1958
Creator: Egorov, L. T.

On the statistical theory of turbulence

Description: A study is made of the spectrum of isotropic turbulence with the aid of the customary method of Fourier analysis. The spectrum of the turbulent motion is derived to the smallest wave lengths, that is, into the laminar region, and correlation functions and pressure fluctuations are calculated. A comparison with experimental results is included. Finally, an attempt is made to derive the numerical value of a constant characteristic of the energy dissipation in isotropic turbulence.
Date: January 1, 1958
Creator: Heisenberg, W

Theory and experiments on supersonic air-to-air ejectors.

Description: A comparison of experiment with theory is made for air ejectors having cylindrical mixing sections and operating under conditions of supersonic primary flow and either mixed or supersonic regimes of mixing. The effect on ejector performance of such parameters as mixer length and cross section, terminating diffuser, primary Mach number, and primary nozzle position is presented in terms of mass flow and pressure ratio.
Date: January 1, 1958
Creator: Fabri, J & Paulon, J

The Principles of Turbulent Heat Transfer

Description: The literature on turbulent heat transfer has in the course of years attained a considerable volume. Since this very complicated problem has not as yet found a complete solution, further studies in this field may be expected. The heat engineer must therefore accomodate himself to a constantly increasing number of theories and formulas. Since the theories generally start from hypothetical assumptions, and since they contain true and false assertions, verified knowledge and pure suppositions often being intermingled in a manner difficult to tell them apart, the specialist had difficulty in forming a correct evaluation of the individual studies. The need therefore arises for a presentation of the problem of turbulent heat transfer which is not initially bound by hypothetical assumptions and in which uninvestigated can be clearly distinguished form each other. Such a presentation will be given in the present treatment. Brief remarks with regard to the development of the theory of local heat transfer are included.
Date: September 1957
Creator: Reichardt, H.

Study of the Micro-Nonuniformity of the Plastic Deformation of Steel

Description: The plastic flow during deformation of real polycrystalline metals has specific characteristics which distinguish the plastic deformation of metals from the deformation of ordinary isotropic bodies. One of these characteristics is the marked micro-nonuniformity of the plastic deformation of metals. P.O. Pashkov demonstrated the presence of a considerable micro-nonuniformity of the plastic deformation of coarse-grained steel wit medium or low carbon content. Analogous results in the case of tension of coarse-grained aluminum were obtained by W. Boas, who paid particular attention to the role of the grain boundaries in plastic flow. The nonuniformit of the plastic deformation in microvolumes was also recorded by T.N. Gudkova and others, on the alloy KhN80T. N.F. Lashko pointed out the nonuniformity of the plastic deformation for a series of pure polycrystalline metals and one-phase alloys. In his later reports, P.O. Pashkov arrives at he conclusion that the nonuniformity of the distribution of the deformation along the individual grains has a significant effect on the strength and plastic characteristics of polycrystalline metals in the process of plastic flow. However, until now there has not existed any systematic investigation of the general rules of the microscopic nonuniformit of plastic deformation even though the real polycrystalline metals are extremely simple with regard to structure. In the present report, an attempt is made to study the micrononuniformity of the flow of polycrystalline metals by the method of statistical analysis of the variation of the frequency diagrams of the nonuniformity of the grains in the process of plastic deformation.
Date: August 1, 1957
Creator: Chechulin, B. B.

Reflection and Refraction of Acoustic Waves by a Shock Wave

Description: The presence of sound waves in one or the other of the fluid regions on either side of a shock wave is made apparent, in the region under superpressure, by acoustic waves (reflected or refracted according to whether the incident waves lie in the region of superpressure or of subpressure) and by thermal waves. The characteristics of these waves are calculated for a plane, progressive, and uniform incident wave. In the case of refraction, the refracted acoustic wave can, according to the incidence, be plane, progressive, and uniform or take the form of an 'accompanying wave' which remains attached to the front of the shock while sliding parallel to it. In all cases, geometrical constructions permit determination of the kinematic characteristics of the reflected or refractive acoustic waves. The dynamic relationships show that the amplitude of the reflected wave is always less than that of the incident wave. The amplitude of the refracted wave, whatever its type, may in certain cases be greater than that of the incident wave.
Date: July 1, 1957
Creator: Brillouin, J.

Effect of Fatigue Crack on Static Strength: 2014-T6, 2024-T4, 6061-T6, 7075-T6 Open-Hole Monobloc Specimens

Description: 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. It is indicated that a 7075-T6 specimen may develop as little as one-third of the expected static tensile strength when the fatigue crack was consumed only one-fourth of the original area. It was found that the static strength was substantially higher for specimens which had stop holes drilled at the end of the fatigue crack.
Date: May 1, 1957
Creator: Nordmark, Glenn E. & Eaton, Ian D.

Wall Interference in a Perforated Wind Tunnel

Description: The theory of cascades, made up of a series of flat plates placed one behind the other, is extended to the case where the impinging stream is not uniform, and the deduced properties of this cascade-flow are then applied to the study of the wall interference between such as cascade-like boundary and a vortex-source type of singularity. It is shown that the induced velocities, produced by the presence of such a wall, are equal to what is obtained by action of a suitably chosen 'reflected' singularity situated on one side of the wall, together with the action of another suitably chosen 'transmitted' singularity placed on the other side. The concepts of a reflection factor and a transmission factor are introduced to characterize various types of tunnel boundary, whether this is composed of solid wall, open and closed sequences, or just a free fluid surface. These ideas are then extended to cover the situation in which a pair of such walls are allowed to coalesce, especially in the event that one of the walls consists of open and closed portions and the other is a fluid surface. This latter particular combination of boundaries is called a perforated wall. Finally, the interference arising from an arbitrary general singularity placed symmetrically in between two such perforated walls is analyzed, and these results are then applied to the determination of the particular kinds of wall geometry that will produce no interference effects in the case of a slender lifting wing and also in the case of a symmetric profile having a finite thickness.
Date: May 1, 1957
Creator: Brescia, Riccardo

The Effect of Solid Admixtures on the Velocity of Motion of a Free Dusty Air Jet

Description: 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. As a result, the rules of velocity change are different for clean and for dusty air flows. The estimation of the influence of the admixture on the velocity of the motion of the flow presents a definitive interest. One of the attempts to estimate that influence on the axial velocity of a free axially symmetrical jet with admixtures was made by Abramovich. Abramovich assumed beforehand that the fine particles of the admixture in the jet are subject to the motion of the air (that is, that the velocity of the admixture is approximately equal to the local velocity of the air); he then took as the basis of his considerations, in solving the problem, the condition that the amount of motion of the two-phase jet must be constant.
Date: April 1, 1957
Creator: Chernov, A. P.

Steady Nuclear Combustion in Rockets

Description: The astrophysical theory of stationary nuclear reactions in stars is applied to the conditions that would be met in the practical engineering cases that would differ from the former, particularly with respect to the much lower combustion pressures, dimensions of the reacting volume, and burnup times. This application yields maximum rates of hear production per unit volume of reacting gas occurring at about 10(exp 8) K in the cases of reactions between the hydrogen isotopes, but yields higher rates for heavier atoms. For the former, with chamber pressures of the order of 100 atmospheres, the energy production for nuclear combustion reaches values of about 10(exp 4) kilocalories per cubic meter per second, which approaches the magnitude for the familiar chemical fuels. The values are substantially lower for heavier atoms, and increase with the square of the combustion pressure. The half-life of the burnup in the fastest reactions may drop to values as low as those for chemical fuels so that, despite the high temperature, the radiated energy can remain smaller than the energy produced, particularly if an inefficiently radiating (i.e., easily completely ionized reacting material like hydrogen), is used. On the other hand, the fraction of completely ionized particles in the gases undergoing nuclear combustion must not exceed a certain upper limit because the densities (approximately 10(exp -10) grams per cubic centimeter)) lie in the range of high vacua and only for the previously mentioned fraction of nonionized particles can mean free paths be retained small enough so that the chamber diameters of several dozen meters will suffice. Under these conditions it appears that continuously maintained stable nuclear reactions at practical pressures and dimensions are fundamentally possible and their application can be visualized as energy sources for power plants and propulsion units.
Date: April 1, 1957
Creator: Saenger, E.

NACA Conference on Aircraft Loads, Structures, and Flutter

Description: This document contains reproductions of technical papers on some of the most recent research results on aircraft loads, flutter, and structures from the NACA laboratories. These papers were presented by members of the staff of the NACA laboratories at the Conference held at the Langley Aeronautical Laboratory March 5, 6, and 7, 1957. The primary purpose of this Conference was to convey to contractors of the military services and others concerned with the design of aircraft these recent research results and to provide those attending an opportunity to discuss the results. The papers in this document are in the same form in which they were presented at the Conference in order to facilitate their prompt distribution. The original presentation and this record are considered as complementary to, rather than as substitutes for, the Committee?s more complete and formal reports. Accordingly, if information from this document is utilized it is requested that this document not be listed as a reference. Individual reports dealing with most of the information presented at the Conference will subsequently be published by NACA and will therefore be suitable as reference material.
Date: March 5, 1957

On the Use of the Harmonic Linearizaiton Method in the Automatic Control Theory

Description: The method of harmonic linearization (harmonic balance), first proposed by N. M. Krylov and N. N. Bogolyubov for the approximate investigation of nonlinear vibrations, has been developed and received wide practical application to problems in the theory of automatic control. Recently, some doubt has been expressed on the legitimacy of application of the method to these problems, and assertions were made on the absence in them of a small parameter of any kind. Nevertheless, the method gives practical, acceptable results and is a simple and powerful means in engineering computations. Hence, the importance of questions arises as to its justification. The underlying principle of the method is the replacement of the given nonlinear equation by a linear equation. In establishing the method, a small parameter is considered whose presence makes it possible to speak, with some degree of approximation, of the solution of this new equation to the solution of the given nonlinear equation. In an article by the author, certain considerations were given on the presence of the small parameter, but this question has not as yet received a final answer. In the present report, a somewhat different approach to the problem is applied that permits: (a) establishing, in the clearest manner, the form of the presence of the small parameter in nonlinear problems of control theory, solvable by the method of harmonic linearization; (b) connecting it with previous intuitive physical concepts (with the "filter property") and extending the class of problems possessing this property; and (c) discussing various generalizations of the method.
Date: January 1, 1957
Creator: Popov, E. P.

A Theoretical Investigation of the Drag of Generalized Aircraft Configurations in Supersonic Flow

Description: It seems possible that, in supersonic flight, unconventional arrangements of wings and bodies may offer advantages in the form of drag reduction. It is the purpose of this report to consider the methods for determining the pressure drag for such unconventional configurations, and to consider a few of the possibilities for drag reduction in highly idealized aircraft. The idealized aircraft are defined by distributions of lift and volume in three-dimensional space, and Hayes' method of drag evaluation, which is well adapted to such problems, is the fundamental tool employed. Other methods of drag evaluation are considered also wherever they appear to offer amplifications. The basic singularities such as sources, dipoles, lifting elements and volume elements are discussed, and some of the useful inter-relations between these elements are presented. Hayes' method of drag evaluation is derived in detail starting with the general momentum theorem. In going from planar systems to spatial systems certain new problems arise. For example, interference between lift and thickness distributions generally appears, and such effects are used to explain the difference between the non-zero wave drag of Sears-Haack bodies and the zero wave drag of Ferrari's ring wing plus central body. Another new feature of the spatial systems is that optimum configurations generally are not unique, there being an infinite family of lift or thickness distributions producing the same minimum drag. However it is shown that all members of an optimum family produce the same flow field in a certain region external to the singularity distribution. Other results of the study indicate that certain spatial distributions may produce materially less wave drag and vortex drag than comparable planar systems. It is not at all certain that such advantages can be realized in practical aircraft designs, but further investigation seems to be warranted.
Date: January 1957
Creator: Graham, E. W.; Lagerstrom, P. A.; Licher, R. M. & Beane, B. J.

Turbulence in the Wake of a Thin Airfoil at Low Speeds

Description: Experiments have been made to determine the nature of turbulence in the wake of a two-dimensional airfoil at low speeds. The experiments were motivated by the need for data which can be used for analysis of the tail-buffeting problem in aircraft design. Turbulent intensity and power spectra of the velocity fluctuations were measured at a Reynolds number of 1.6 x 10(exp 5) for several angles of attack. Total-head measurements were also obtained in an attempt to relate steady and fluctuating wake properties. Mean-square downwash was found to have nearly the same dependence on vertical position in the wake as that shown by total-head loss. For this particular wing, turbulent intensity, integrated across the wake, increased roughly as the 3/2 power of the drag coefficient. Power-spectrum measurements indicated a decrease in frequency as wing angle of attack was increased. The average frequency in the wake was proportional to the ratio of mean wake velocity to wake width.
Date: January 1, 1957
Creator: Campbell, George S.

On the Calculation of Shallow Shells

Description: This paper considers a sufficiently thin shallow shell of nonzero Gaussian curvature. It also presents a system of symmetrically constructed differential equations, constructed by the mixed method through the stress function and the displpacement function.
Date: December 1, 1956
Creator: Ambartsumyan, S. A.